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Boolean Valued Models, Boolean Valuations, and Löwenheim-Skolem Theorems
Boolean-valued models for first-order languages generalize two-valued models, in that the value range is allowed to be any complete Boolean algebra...
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Boolean-Like Algebras of Finite Dimension: From Boolean Products to Semiring Products
We continue the investigation, initiated in Salibra et al. (Found Sci, 2020), of Boolean-like algebras of dimension n (...
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On the Representation of Boolean Magmas and Boolean Semilattices
A magma is an algebra with a binary operation \(\cdot \)...
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Boolean Background
This chapter discusses Boolean algebras and the Boolean notions used in this book. The first section is meant for those who want to get to the main...
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On J. Czelakowski’s Contributions to Quantum Logic and the Foundation of Quantum Mechanics
This paper provides an overview of Janusz Czelakowski’s contributions to the theory of partial Boolean (...
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On the (Complete) Reasons Behind Decisions
Recent work has shown that the input-output behavior of some common machine learning classifiers can be captured in symbolic form, allowing one to...
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On Computing Structural and Behavioral Complexities of Threshold Boolean Networks
Various threshold Boolean networks (TBNs), a formalism used to model different types of biological networks (genes notably), can produce similar...
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From Contact Relations to Modal Operators, and Back
One of the standard axioms for Boolean contact algebras says that if a region
x is in contact with the join ofy andz , thenx is in contact with at... -
On the Origin of Venn Diagrams
In this paper we argue that there were several currents, ideas and problems in 19th-century logic that motivated John Venn to develop his famous...
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A Minimal Probability Space for Conditionals
One of central problems in the theory of conditionals is the construction of a probability space, where conditionals can be interpreted as events and...
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A Logic of “Black Box” Classifier Systems
Binary classifiers are traditionally studied by propositional logic ( \(\textsf{PL}\)...
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Representability of Kleene Posets and Kleene Lattices
A Kleene lattice is a distributive lattice equipped with an antitone involution and satisfying the so-called normality condition. These lattices were...
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The Orthologic of Epistemic Modals
Epistemic modals have peculiar logical features that are challenging to account for in a broadly classical framework. For instance, while a sentence...
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A Combinatorial Exploration of Boolean Dynamics Generated by Isolated and Chorded Circuits
Most studies of motifs of biological regulatory networks focus on the analysis of asymptotical behaviours (attractors, and even often only stable...
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Unwinding Modal Paradoxes on Digraphs
The unwinding that Cook (J. Symbol. Log. 69 (3), 767–774
2004 ) proposed is a simple but powerful method of generating new paradoxes from known ones.... -
Dualities for Regular Varieties
Mathematicians often try to shed new light on the properties of abstract or unfamiliar structures by somehow linking them to more concrete or better...
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A Simple Logic of the Hide and Seek Game
We discuss a simple logic to describe one of our favourite games from childhood, hide and seek, and show how a simple addition of an equality...
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Minimisation in Logical Form
Recently, two apparently quite different duality-based approaches to automata minimisation have appeared. One is based on ideas that originated from...
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Recognizability in Residuated Lattices
The objective of this work is to show that modules over a fixed residuated lattice...